Abstract
In this study we numerically examine the mixed convection stagnation-point flow of a nanofluid over a vertical stretching/shrinking sheet in the presence of suction, thermal radiation and a heat source/sink. Three distinct types of nanoparticles, copper (Cu), alumina (Al2O3) and titania (TiO2), were investigated with water as the base fluid. The governing partial differential equations were converted into ordinary differential equations with the aid of similarity transformations and solved numerically by utilizing the bvp4c programme in MATLAB. Dual (upper and lower branch) solutions were determined within a particular range of the mixed convection parameters in both the opposing and assisting flow regions and a stability analysis was carried out to identify which solutions were stable. Accordingly, solutions were gained for the reduced skin friction coefficients, the reduced local Nusselt number, along with the velocity and temperature profiles for several values of the parameters, which consists of the mixed convection parameter, the solid volume fraction of nanoparticles, the thermal radiation parameter, the heat source/sink parameter, the suction parameter and the stretching/shrinking parameter. Furthermore, the solutions were presented in graphs and discussed in detail.
Highlights
Mixed convection flows or a combination of forced and free convections exists in numerous transport operations, both naturally occurring and in engineering applications
The derived nonlinear ordinary differential equations given in Equations (10) and (11) along with the boundary conditions given in (12) were solved numerically and were obtained using the bvp4c programme in MATLAB (Matlab R2015a, MathWorks, Natick, MA, USA) for the selected values of the mixed convection parameter λ, solid volume fraction of nanoparticles φ, thermal radiation parameter
It is further confirmed that the presence of nanoparticles, heat sink, suction and stretching sheet could decelerate the separation of the boundary layer, while the presence of thermal radiation, heat source and shrinking sheet could accelerate the separation of the boundary layer
Summary
Mixed convection flows or a combination of forced and free convections exists in numerous transport operations, both naturally occurring and in engineering applications Such applications for example, include heat exchangers, solar collectors, nuclear reactors, atmospheric boundary layer flow, nanotechnology, electronic apparatus, etc. These operations occur during the effects of buoyancy forces in forced convections or the effects of forced flow in free convections become substantial. Over the past several decades, most research in mixed convection flow analysis has emphasised the occurrence of dual solutions for a particular range of the buoyancy (mixed convection) parameter in the opposing flow region, such as in the research by Ramachandran et al [1], Merkin and Mahmood [2], Devi et al [3] and Lok et al [4]. Various other researches have stated the occurrence of dual solutions in the mixed convection flow in different configurations, namely by Roşca et al [7], Rahman et al [8] and recently by Abbasbandy et al [9]
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